State the position of the lines for (2x-3y=5) and (4x-6y=7).
Answer and explanation
Correct answer: Distinct parallel lines
Comparing the coefficients, \(a_1/a_2=2/4=1/2\) and \(b_1/b_2=(-3)/(-6)=1/2\), but \(c_1/c_2=5/7\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), which is the condition for distinct parallel lines. Therefore, option C is correct. Option B is incorrect because coincident lines require all three ratios to be equal. Exam tip: If \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the lines are distinct and parallel.
Frequently asked questions
What is the correct answer to this question?
Distinct parallel lines
Why is this the correct answer?
Comparing the coefficients, \(a_1/a_2=2/4=1/2\) and \(b_1/b_2=(-3)/(-6)=1/2\), but \(c_1/c_2=5/7\). Thus, \(a_1/a_2=b_1/b_2\ne c_1/c_2\), which is the condition for distinct parallel lines. Therefore, option C is correct. Option B is incorrect because coincident lines require all three ratios to be equal. Exam tip: If \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the lines are distinct and parallel.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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